sml-data-show

�k

1
data.f


1
summary(data.f)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
##  Sex             Equipment           Age           AgeClass    
## F:191337 Multi-ply : 5099 Min. : 0.50 20-24 :33773
## M: 0 Raw :103914 1st Qu.:21.00 15-19 :29307
## Single-ply: 63461 Median :27.50 25-29 :27386
## Straps : 0 Mean :30.61 30-34 :19909
## Wraps : 18863 3rd Qu.:38.50 35-39 :15863
## Max. :97.00 (Other):44154
## NA's :20945
## BodyweightKg Best3SquatKg Best3BenchKg Best3DeadliftKg
## Min. : 15.88 Min. :-252.5 Min. :-197.50 Min. :-190.0
## 1st Qu.: 55.90 1st Qu.: 95.0 1st Qu.: 52.50 1st Qu.: 115.0
## Median : 64.74 Median : 115.0 Median : 65.00 Median : 135.0
## Mean : 67.63 Mean : 120.2 Mean : 69.85 Mean : 136.3
## 3rd Qu.: 74.90 3rd Qu.: 142.5 3rd Qu.: 82.50 3rd Qu.: 155.0
## Max. :184.90 Max. : 387.5 Max. : 272.50 Max. : 315.0
## NA's :52295 NA's :15712 NA's :38396
## TotalKg
## Min. : 7.5
## 1st Qu.:170.0
## Median :282.5
## Mean :267.1
## 3rd Qu.:350.0
## Max. :930.0
## NA's :7689

�k

1
data.m


1
summary(data.m)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
##  Sex             Equipment           Age           AgeClass     
## F: 0 Multi-ply : 38902 Min. : 0.00 20-24 :105154
## M:559580 Raw :260557 1st Qu.:21.50 15-19 : 82074
## Single-ply:201147 Median :28.00 25-29 : 77263
## Straps : 12 Mean :31.76 30-34 : 56935
## Wraps : 58962 3rd Qu.:40.00 35-39 : 41684
## Max. :95.50 (Other):140077
## NA's : 56393
## BodyweightKg Best3SquatKg Best3BenchKg Best3DeadliftKg
## Min. : 17.69 Min. :-477.5 Min. :-522.5 Min. :-410.0
## 1st Qu.: 75.00 1st Qu.: 170.0 1st Qu.: 115.0 1st Qu.: 195.0
## Median : 89.40 Median : 210.0 Median : 145.0 Median : 230.0
## Mean : 91.69 Mean : 213.5 Mean : 149.0 Mean : 228.5
## 3rd Qu.:104.40 3rd Qu.: 252.5 3rd Qu.: 180.0 3rd Qu.: 265.0
## Max. :258.00 Max. : 575.0 Max. : 488.5 Max. : 457.5
## NA's :213599 NA's :61337 NA's :177163
## TotalKg
## Min. : 5.0
## 1st Qu.: 210.0
## Median : 470.0
## Mean : 441.6
## 3rd Qu.: 617.5
## Max. :1367.5
## NA's :37095

�k�`��

1
data.f.Squat


1
summary(data.f.Squat)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
##  Sex             Equipment          Age           AgeClass    
## F:138748 Multi-ply : 2712 Min. : 0.50 20-24 :26946
## M: 0 Raw :72951 1st Qu.:20.50 15-19 :23743
## Single-ply:44604 Median :26.50 25-29 :20581
## Straps : 0 Mean :29.26 30-34 :14013
## Wraps :18481 3rd Qu.:36.50 35-39 :10770
## Max. :91.50 (Other):27031
## NA's :15664
## BodyweightKg Best3SquatKg Best3BenchKg Best3DeadliftKg
## Min. : 21.77 Min. : 11.3 Min. :-190.00 Min. :-190.0
## 1st Qu.: 56.00 1st Qu.: 95.0 1st Qu.: 52.50 1st Qu.: 115.0
## Median : 64.90 Median :115.0 Median : 64.86 Median : 136.1
## Mean : 67.73 Mean :120.8 Mean : 67.80 Mean : 137.2
## 3rd Qu.: 74.90 3rd Qu.:142.5 3rd Qu.: 80.00 3rd Qu.: 156.5
## Max. :184.20 Max. :387.5 Max. : 242.67 Max. : 315.0
## NA's :2185 NA's :1977
## TotalKg
## Min. : 24.95
## 1st Qu.:265.00
## Median :315.00
## Mean :325.33
## 3rd Qu.:375.00
## Max. :930.00
## NA's :2740

�k�`��

1
data.m.Squat


1
summary(data.m.Squat)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
##  Sex             Equipment           Age           AgeClass    
## F: 0 Multi-ply : 16635 Min. : 0.00 20-24 :76408
## M:345026 Raw :141920 1st Qu.:20.50 15-19 :59834
## Single-ply:129240 Median :25.50 25-29 :50629
## Straps : 0 Mean :29.46 30-34 :33120
## Wraps : 57231 3rd Qu.:35.50 35-39 :21869
## Max. :95.50 (Other):66298
## NA's :36868
## BodyweightKg Best3SquatKg Best3BenchKg Best3DeadliftKg
## Min. : 17.69 Min. : 7.5 Min. :-365.0 Min. :-347.5
## 1st Qu.: 74.80 1st Qu.:170.0 1st Qu.: 112.5 1st Qu.: 197.5
## Median : 88.99 Median :210.0 Median : 140.0 Median : 230.0
## Mean : 90.70 Mean :214.7 Mean : 142.3 Mean : 229.1
## 3rd Qu.:103.10 3rd Qu.:252.5 3rd Qu.: 170.0 3rd Qu.: 265.0
## Max. :258.00 Max. :575.0 Max. : 455.9 Max. : 457.5
## NA's :8606 NA's :9948
## TotalKg
## Min. : 18.14
## 1st Qu.: 482.50
## Median : 577.50
## Mean : 584.56
## 3rd Qu.: 680.00
## Max. :1367.50
## NA's :11697

�k����

1
data.f.Bench


1
summary(data.f.Bench)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
##  Sex             Equipment          Age           AgeClass    
## F:175333 Multi-ply : 4466 Min. : 0.50 20-24 :31436
## M: 0 Raw :93846 1st Qu.:20.50 15-19 :27391
## Single-ply:58735 Median :27.50 25-29 :25039
## Straps : 0 Mean :30.42 30-34 :17945
## Wraps :18286 3rd Qu.:38.50 35-39 :14158
## Max. :97.00 (Other):39578
## NA's :19786
## BodyweightKg Best3SquatKg Best3BenchKg Best3DeadliftKg
## Min. : 18.90 Min. :-252.5 Min. : 7.50 Min. :-190.0
## 1st Qu.: 55.90 1st Qu.: 95.0 1st Qu.: 52.50 1st Qu.: 115.0
## Median : 64.70 Median : 115.0 Median : 65.00 Median : 135.0
## Mean : 67.66 Mean : 120.5 Mean : 70.08 Mean : 136.8
## 3rd Qu.: 74.90 3rd Qu.: 142.5 3rd Qu.: 82.50 3rd Qu.: 155.0
## Max. :184.20 Max. : 387.5 Max. :272.50 Max. : 315.0
## NA's :38863 NA's :33886
## TotalKg
## Min. : 7.5
## 1st Qu.:205.0
## Median :290.0
## Mean :275.5
## 3rd Qu.:355.0
## Max. :930.0
## NA's :2416

�k����

1
data.m.Bench


1
summary(data.m.Bench)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
##  Sex             Equipment           Age           AgeClass     
## F: 0 Multi-ply : 32145 Min. : 0.00 20-24 : 95264
## M:496743 Raw :228584 1st Qu.:21.00 15-19 : 74543
## Single-ply:179763 Median :27.50 25-29 : 68278
## Straps : 0 Mean :31.55 30-34 : 49461
## Wraps : 56251 3rd Qu.:40.00 35-39 : 35870
## Max. :95.50 (Other):121602
## NA's : 51725
## BodyweightKg Best3SquatKg Best3BenchKg Best3DeadliftKg
## Min. : 17.69 Min. :-445.0 Min. : 5.0 Min. :-347.5
## 1st Qu.: 75.00 1st Qu.: 170.0 1st Qu.:115.7 1st Qu.: 197.3
## Median : 89.30 Median : 210.0 Median :145.0 Median : 230.0
## Mean : 91.42 Mean : 214.0 Mean :150.0 Mean : 228.8
## 3rd Qu.:104.11 3rd Qu.: 252.5 3rd Qu.:180.0 3rd Qu.: 263.1
## Max. :258.00 Max. : 575.0 Max. :488.5 Max. : 457.5
## NA's :160784 NA's :150085
## TotalKg
## Min. : 5.0
## 1st Qu.: 215.0
## Median : 492.5
## Mean : 456.4
## 3rd Qu.: 627.5
## Max. :1367.5
## NA's :8330

�k�w��

1
data.f.Deadlift


1
summary(data.f.Deadlift)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
##  Sex             Equipment          Age           AgeClass    
## F:152867 Multi-ply : 3063 Min. : 0.50 20-24 :28662
## M: 0 Raw :84796 1st Qu.:20.50 15-19 :24798
## Single-ply:46676 Median :27.00 25-29 :22521
## Straps : 0 Mean :29.84 30-34 :15779
## Wraps :18332 3rd Qu.:37.00 35-39 :12385
## Max. :97.00 (Other):32289
## NA's :16433
## BodyweightKg Best3SquatKg Best3BenchKg Best3DeadliftKg
## Min. : 15.88 Min. :-252.5 Min. :-185.00 Min. : 10.0
## 1st Qu.: 56.00 1st Qu.: 95.0 1st Qu.: 52.50 1st Qu.:115.0
## Median : 65.20 Median : 115.0 Median : 63.50 Median :135.0
## Mean : 67.96 Mean : 120.5 Mean : 67.69 Mean :136.5
## 3rd Qu.: 75.00 3rd Qu.: 142.5 3rd Qu.: 78.00 3rd Qu.:155.0
## Max. :184.90 Max. : 387.5 Max. : 242.67 Max. :315.0
## NA's :16016 NA's :11333
## TotalKg
## Min. : 10.0
## 1st Qu.:247.5
## Median :305.0
## Mean :308.7
## 3rd Qu.:367.4
## Max. :930.0
## NA's :2730

�k�w��

1
data.m.Deadlift


1
summary(data.m.Deadlift)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
##  Sex             Equipment           Age           AgeClass    
## F: 0 Multi-ply : 18808 Min. : 0.00 20-24 :81632
## M:381875 Raw :173476 1st Qu.:20.50 15-19 :63983
## Single-ply:133584 Median :26.00 25-29 :56058
## Straps : 12 Mean :30.01 30-34 :37408
## Wraps : 55995 3rd Qu.:36.50 35-39 :25114
## Max. :95.50 (Other):79191
## NA's :38489
## BodyweightKg Best3SquatKg Best3BenchKg Best3DeadliftKg
## Min. : 17.69 Min. :-445.0 Min. :-362.5 Min. : 10.0
## 1st Qu.: 75.00 1st Qu.: 170.0 1st Qu.: 112.5 1st Qu.:195.0
## Median : 89.10 Median : 208.7 Median : 140.0 Median :230.0
## Mean : 91.02 Mean : 213.8 Mean : 142.6 Mean :229.2
## 3rd Qu.:103.45 3rd Qu.: 252.5 3rd Qu.: 170.0 3rd Qu.:265.0
## Max. :242.40 Max. : 575.0 Max. : 488.5 Max. :457.5
## NA's :46844 NA's :35208
## TotalKg
## Min. : 10.0
## 1st Qu.: 440.0
## Median : 555.0
## Mean : 548.8
## 3rd Qu.: 665.0
## Max. :1367.5
## NA's :6482

�k�T������

1
data.f.SBD


1
summary(data.f.SBD)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
##  Sex             Equipment          Age           AgeClass    
## F:135805 Multi-ply : 2604 Min. : 0.50 20-24 :26377
## M: 0 Raw :71699 1st Qu.:20.50 15-19 :23181
## Single-ply:43413 Median :26.50 25-29 :20176
## Straps : 0 Mean :29.28 30-34 :13711
## Wraps :18089 3rd Qu.:36.50 35-39 :10542
## Max. :91.50 (Other):26497
## NA's :15321
## BodyweightKg Best3SquatKg Best3BenchKg Best3DeadliftKg
## Min. : 21.77 Min. : 11.3 Min. :-190.0 Min. :-190.0
## 1st Qu.: 56.00 1st Qu.: 95.0 1st Qu.: 52.5 1st Qu.: 115.0
## Median : 64.95 Median :115.0 Median : 65.0 Median : 136.1
## Mean : 67.75 Mean :120.7 Mean : 67.9 Mean : 137.2
## 3rd Qu.: 74.90 3rd Qu.:142.5 3rd Qu.: 80.0 3rd Qu.: 157.0
## Max. :184.20 Max. :387.5 Max. : 242.7 Max. : 315.0
##
## TotalKg
## Min. : 40.8
## 1st Qu.:267.5
## Median :315.0
## Mean :326.1
## 3rd Qu.:375.0
## Max. :930.0
## NA's :343

�k�T������

1
data.m.SBD


1
summary(data.m.SBD)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
##  Sex             Equipment           Age           AgeClass    
## F: 0 Multi-ply : 15528 Min. : 0.00 20-24 :73811
## M:332520 Raw :138195 1st Qu.:20.50 15-19 :57794
## Single-ply:123355 Median :25.50 25-29 :48776
## Straps : 0 Mean :29.45 30-34 :31808
## Wraps : 55442 3rd Qu.:35.50 35-39 :20904
## Max. :95.50 (Other):63826
## NA's :35601
## BodyweightKg Best3SquatKg Best3BenchKg Best3DeadliftKg
## Min. : 17.69 Min. : 7.5 Min. :-362.5 Min. :-347.5
## 1st Qu.: 74.80 1st Qu.:170.0 1st Qu.: 112.5 1st Qu.: 197.5
## Median : 88.90 Median :210.0 Median : 140.0 Median : 230.0
## Mean : 90.65 Mean :214.3 Mean : 142.6 Mean : 229.2
## 3rd Qu.:103.00 3rd Qu.:252.5 3rd Qu.: 170.0 3rd Qu.: 265.0
## Max. :242.40 Max. :575.0 Max. : 455.9 Max. : 457.5
##
## TotalKg
## Min. : 38.6
## 1st Qu.: 485.0
## Median : 577.5
## Mean : 586.7
## 3rd Qu.: 682.5
## Max. :1367.5
## NA's :1303

機器學習-1

在統計機器學習這門課,老師出了一個小作業,讓我們用$N((1, 0)^{T} , I)$ 和$N((0, 1)^{T} , I)​$ 生成各10組資料

然後各分一類,每類用隨機的方式抽100次作為$m_{k}$ 做$N(m_{k}, I/5)$ 生成共200組資料,我將以$N((1, 0)^{T} , I)$ 生的的資料的類別令為0,另一組為1。

這200組資料就是我們的train data

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
library(MASS)
library(class)

x0<- MASS::mvrnorm(n=10, mu = c(1,0), Sigma = diag(2))
x1<- MASS::mvrnorm(n=10, mu = c(0,1), Sigma = diag(2))
#make data
make.data<-function(x0,x1,n,m,Sigma1 = diag(2)/5,Sigma2 = diag(2)/5){
r<-length(x0[,1])
x<-matrix(0,n+m,2)
for(i in 1:n){
s<-sample(1:r,1)
x[i,]=MASS::mvrnorm(n=1, mu = x0[s,], Sigma = Sigma1)
}
r<-length(x1[,1])
for(i in 1:m){
s<-sample(1:r,1)
x[i+n,]=MASS::mvrnorm(n=1, mu = x1[s,], Sigma = Sigma2)
}
y<-matrix(c(rep(0,n),rep(1,m)),n+m,1)
data<-data.frame(y,x)
return(data)
}
train.data<-make.data(x0,x1,100,100,diag(2)/5,diag(2)/5)

再以同樣的方式生成10000組資料,這是我們的test data。

1
train.data<-make.data(x0,x1,5000,5000,diag(2)/5,diag(2)/5)

然後我們就要開始用機器學習的方法了,這次只有要看誤差的機率,不過現在不會什麼,只有用基礎的迴歸和KNN

以下是迴歸的

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
#迴歸
er.lm<-function(train.data,test.data){
q<-lm(train.data[,1]~train.data[,2]+train.data[,3],train.data)
z<-data.frame(q$coefficients)$ q.coefficients
t<-matrix(0,2,2)
rownames(t)<-c("blue.lm","orange.lm")
colnames(t)<-c("blue","orange")
n<-length(test.data[,1])
for(i in 1:n){
a<-z[1]+z[2]*test.data[i,2]+z[3]*test.data[i,3]
if(a>=(1/2)){
a=1
}else{
a=0
}
if(test.data[i,1]==0){
if(a==0){
t[1,1]<-t[1,1]+1
}else{
t[2,1]<-t[2,1]+1
}
}else{
if(a==1){
t[2,2]<-t[2,2]+1
}else{
t[1,2]<-t[1,2]+1
}
}
}
return(t/n)
}
er.lm(train.data,train.data)
er.lm(train.data,test.data)

以下是KNN的,因為這個作業,老師有希望我們做出類似課本裡面的圖,所以後面K的選擇是大致上參照課本上面選的K,做圖的方法還沒想好。

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
#KNN
er.knn<-function(train.data,test.data,k){
n<-length(test.data[,1])
y<-knn(train.data[,2:3],test.data[,2:3],train.data[,1],k=k)
e<-0
for(i in 1:n){
if(y[i]!=test.data[i,1]){
e=e+1
}
}
return(e/n)
}


n.er.knn<-function(train.data,test.data,k){
er.test<-c()
for(i in 1:length(k)){
er.test[i]<-er.knn(train.data,test.data,k[i])
}
return(er.test)
}
k<-1:200
data.frame(k,n.er.knn(k,er.knn))

因為老師要我們去試更改$\Sigma$ 會造成甚麼影響

所以我把上面的function整合進了一個function裡面

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
error<-function(mu1= c(1,0),mu2 = c(0,1)
,Sigma1 = diag(2),Sigma2 = diag(2)
,n1=100,m1=100,n2=5000,m2=5000
,Sigma3=diag(2)/5,Sigma4=diag(2)/5
,k=1:200){
x0<- MASS::mvrnorm(n=10, mu = mu1, Sigma = Sigma1)
x1<- MASS::mvrnorm(n=10, mu = mu2, Sigma = Sigma1)
train.data<-make.data(x0,x1,n1,m1,Sigma3,Sigma4)
test.data<-make.data(x0,x1,n2,m2,Sigma3,Sigma4)

train.lm<-er.lm(train.data,train.data)
test.lm<-er.lm(train.data,test.data)

train.knn.er<-n.er.knn(train.data,train.data,k)
test.knn.er<-n.er.knn(train.data,test.data,k)
knn.er<-data.frame(k,train.knn.er,test.knn.er)
err<-list(train.lm=train.lm,test.lm=test.lm,knn.er=knn.er)
return(err)
}

若是單獨輸入

1
error()

就是原本的程式,不過這個跑很慢,所以就沒繼續做下去了

統計計算-2

老師還安排了另一個作業,要我們去對一個函數做0到無限大的積分。

以下是函數

1
2
3
4
g<-function(x){
y<-exp(-x)*(exp(cos(x^2)))^2
return(y)
}

這是這個函數大概的圖形

因為我的function沒辦法處理無限大的情況,所以我就用逼近的方式去逼近這個解。

老師要求誤差要在$10^{-3}$ 以下,我考慮我積分範圍後的一單位距離的積分值,如果這個積分值足夠小的話,那誤差應該可以控制在$10^{-3}$ 以下

積分的方式,我採用上次的Simpson法

1
2
3
4
5
6
7
8
9
10
11
12
13
14
Simpson<-function(f,a,b,n){
k<-0
h<-(b-a)/n
for(i in 0:n){
if(i==0||i==n){
k<-k+(h/3)*f(a+i*h)
}else if(i%%2==1){
k<-k+(h/3)*4*(f(a+i*h))
}else{
k<-k+(h/3)*2*(f(a+i*h))
}
}
return(k)
}

這是具體的程式碼

1
2
3
4
5
6
7
x<-1
b<-1
while(x>10^(-5)){
x<-Simpson(g,0,b+1,10^4)-Simpson(g,0,b,10^4)
b<-b+1
}
Simpson(g,0,b+1,10^4)

出來的結果為 $4.720507$

統計計算-1

在統計計算這門課中
老師要求我們用R寫一個積分的function
老師給我們3個方法
一、左右離曼積分
二、梯型法
三、simpson法
以下是我寫的程式
一、左右離曼積分
以離曼積分的概念作積分,為了方便做計算,就不去找黎曼上和或下和,而是以左或右的$f(x)​$的值作為高

1
2
3
4
5
6
7
8
integral<-function(f,a,b,n){
k<-0
m<-(b-a)/n
for(i in 1:n){
k<-k+f(a+i*m)*(1/n)
}
return(k)
}

二、梯型法
一樣是離曼積分的概念,不過這次以有左右的$f(x)​$的值作為梯型的上底和下底。

1
2
3
4
5
6
7
8
Trapezoid<-function(f,a,b,n){
k<-0
m<-(b-a)/n
for(i in 1:n){
k<-k+(f(a+i*m)+f(a+(i-1)*m))*(1/n)/2
}
return(k)
}

三、simpson法
我看不太懂這個,我只是照公式寫

1
2
3
4
5
6
7
8
9
10
11
12
13
14
Simpson<-function(f,a,b,n){
k<-0
h<-(b-a)/n
for(i in 0:n){
if(i==0||i==n){
k<-k+(h/3)*f(a+i*h)
}else if(i%%2==1){
k<-k+(h/3)*4*(f(a+i*h))
}else{
k<-k+(h/3)*2*(f(a+i*h))
}
}
return(k)
}

老師給我們的$f(x)$

1
2
3
4
f<- function(x){
y<-exp(-x^2)
return(y)
}

積分範圍是$(0,1)$ 將它分成4,8,16,32等分

1
2
3
a<-0
b<-1
x<-c(4,8,16,32)

老師要我們去算誤差 和不同等分的誤差之間的比值

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
x1<-c()
for(i in 1:length(x)){
x1[i]<-integral(f,a,b,x[i])-0.746824132812427
}
x11<-c(NA)
for(i in 2:length(x)){
x11[i]<-x1[i-1]/x1[i]
}
x2<-c()
for(i in 1:length(x)){
x2[i]<-Trapezoid(f,a,b,x[i])-0.746824132812427
}
x21<-c(NA)
for(i in 2:length(x)){
x21[i]<-x2[i-1]/x2[i]
}
x3<-c()
for(i in 1:length(x)){
x3[i]<-Simpson(f,a,b,x[i])-0.746824132812427
}
x31<-c(NA)
for(i in 2:length(x)){
x31[i]<-x3[i-1]/x3[i]
}

c<-matrix(c(x,x1,x11,x2,x21,x3,x31),nrow=4, ncol=7)
View(c)
n $I_{R_{n}}$ $I_{T_{n}}$ $I_{S_{n}}$
error ratio error ratio error ratio
4 -0.082855105 -3.840035e-03 3.124698e-05
8 -0.040466053 2.047521 -9.585180e-04 4.006221 1.987715e-06 15.72005
16 -0.019993303 2.023980 -2.395360e-04 4.001561 1.246233e-07 15.94979
32 -0.009936762 2.012054 -5.987816e-05 4.000391 7.794558e-09 15.98850